Within months of Kazimir Malevich’s death in May 1935, his paintings began to disappear. As Stalin enforced Socialist Realism as the official cultural doctrine, curators hid the artist’s radical work to protect it from being seized and destroyed.

His most infamous painting, the Black Square, would not be exhibited again until the 1980s. This work had scandalised audiences when Malevich first unveiled it in 1915. It was a dramatic rejection of all pictorial conventions: the ultimate nihilistic statement.

Tate Modern’s expansive retrospective is the first opportunity to view many of Malevich’s iconic paintings in the UK. It’s not all austere minimalism though, for Malevich’s formative influences were Monet, Cezanne, Picasso, Matisse and Van Gogh.

Malevich’s earliest paintings are packed with colour and expressive brushstrokes. Church (1905) is so densely textured that the rippled paint casts shadows upon itself, creating drama in an otherwise subtle scene of dappled sunlight falling on a church. Portrait of a Man (1908) is a loose patchwork of vibrant colours, made with scrabbling brushstrokes this way and that.

However, Malevich wasn’t satisfied with imitating the European avant-garde; he wanted to produce authentically Russian modernist paintings. He developed the hybrid style of Cubo-Futurism and applied it to provincial landscapes and scenes of peasant life in startling works such as Morning in the Village After Snowstorm (1912).

For this retrospective, Tate Modern has reunited nine of the paintings from Malevich’s first exhibition of Suprematist works in 1915. Wonderfully, they are presented in a similar manner to the original display.

Black Square looms down from the highest corner, the traditional place to display sacred icons in domestic dwellings. Curator Achim Borchardt-Hume sees this seminal work “as enigmatic, baffling and radical an idea today as it was almost a century ago.”

Malevich declared Black Square to be the origin of Suprematism, his new system of non-objective art, which featured stark geometric forms floating in infinite white space. In works such as Suprematist Composition: Airplane Flying (1915) Malevich employed foreshortening and scale as methods of spatial representation, so that the coloured forms appear to move towards or away from the viewer. The result is a seemingly boundless and mysterious space.

Later in his life Malevich returned to figurative painting, a shift which is sometimes viewed as a concession to the demands of the political regime. However, these wonderful works are clearly indebted to his geometric abstractions: Female Torso (1928-9) is an elegant and minimal composition comprising a black oval, a black trapezium and a green rectangle.

Malevich’s most surprising works are saved for last: Renaissance-style portraits. This series - which includes portraits of his wife and mother, painted in the few years before the artist’s death - is unexpectedly moving.

Malevich had not forgone his avant-garde stance, however: these final portraits were signed not with his name, but with the symbol of the black square.

This fantastic retrospective is a rare opportunity to view hundreds of Malevich’s paintings and drawings, and to learn more about the man behind Suprematism: it should not be missed.

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